An Phu / Thao Dien (District 2) is currently the main expat area for western lifestyle. Located at just about 15min. from downtown past the Saigon bridge, it is a preferred place for thoses seeking quietness, whether it be by choosing large houses with private garden and pool or living in compounds.
Phu My Hung (District 7) is also a good area (also the main schools are in D2). This is the new Saigon with well organized streets and security at every corners. The house are usually smaller and most don't have a pool and large size garden. The plus of this area is that it has more shopping options than in D2.